Lesson 18 | Multiplication and Division, Part 2 | 3rd Grade Mathematics

Objective

Multiply one-digit whole numbers by two-digit whole numbers using the associative and distributive properties.

Common Core Standards

Core Standards

The core standards covered in this lesson

3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Number and Operations in Base Ten

3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

3.OA.A.4 — Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?

Operations and Algebraic Thinking

3.OA.A.4 — Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)

Operations and Algebraic Thinking

3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Make use of structure by using the associative property to decompose two-digit numbers in a multiplication problem into smaller factors, then multiply those values in any order (MP.7).
Make use of structure by using the distributive property to decompose the two-digit number in a multiplication problem into a sum or difference of benchmark numbers, multiplying those values separately by the other factor, then adding or subtracting, respectively, those products to give the overall product (MP.7).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Most of the computations in this lesson involve multiplication within 100, an expectation of this grade level, but involve teen numbers, arguably beyond the scope of 3rd grade standards. However, students have all of the skills needed to solve problems of this nature, including multiplication of single-digit number by multiples of ten (3.NBT.3), fluency with multiplication of two one-digit numbers (3.OA.7), and the application of the associative property and distributive property to multiply (3.OA.5). Thus, by extending the work of previous lessons to simple cases of multiplying a one-digit number by a two-digit number, it provides an opportunity to connect two domains in the grade, 3.OA and 3.NBT. It also nicely prepares students for extensive work with multi-digit multiplication in Grade 4.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Latonia and Floyd are trying to solve $$5 \times 12$$. Here are their strategies.

Latonia:

$$ \begin{align} 5\times 12 &= 5\times (10+2) \\ &= (5\times10)+(5\times2) \\ &= 50 + 10 \\ &= 60 \end{align}$$

Floyd:

$$ \begin{align} 5\times12&= 5\times(2\times6) \\ &= (5\times2) \times 6 \\ &= 10\times 6 \\ &= 60 \end{align}$$

What is similar about these strategies? What is different?

Guiding Questions

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Problem 2

To find the value of $$2\times37$$, Mel started by writing this equation:

$$2\times30=60$$

Describe or show what Mel would do to finish finding the value of $$2\times37$$.

Guiding Questions

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References

Illustrative Mathematics Multiply Numbers Larger than 20 — Grade 3 Unit 4 Lesson 16 Activity 2

Multiply Numbers Larger than 20, accessed on Aug. 24, 2022, 6:21 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your work.

a. $$18\times 3=$$ _____

b. _____ $$=4\times16$$

c. _____ $$=14\times 5$$

d. $$6\times 15=$$ _____

e. _____ $$=6\times 21$$

f. $$19\times 7=$$ _____

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

In #1, how do the computations on the bottom make the computations on the top easier?
In #4, how did Marlys convert this to an easier problem?
Which strategy did you tend to rely on in #5? For which problems were certain strategies not possible to use? Why?
In #8, how did Charlotte convert this to an easier problem?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Decide whether each expression is equal to $$3\times 14$$. Select whether the expression is True or False.

	True	False
$$3\times (10+4)$$
$$6\times 11$$
$$(3\times10)+4$$
$$(3\times2)\times7$$
$$3+(10\times4)$$

Problem 2

Solve. Show or explain your work.

$$28\times 5$$

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 17

Lesson 19

Lesson Map

Topic A: Introduction to The Properties of Operations

Study commutativity to find known facts of 6, 7, 8, and 9.

3.OA.B.5 3.OA.D.9

Understand the zero and identity properties of multiplication.

3.OA.A.4 3.OA.B.5 3.OA.C.7 3.OA.D.9

Understand the role of parentheses and apply to solving problems.

3.OA.B.5 3.OA.D.8

Introduce the distributive property of multiplication.

3.OA.B.5 3.OA.D.9

Introduce the associative property of multiplication.

3.OA.B.5 3.OA.D.9

Topic B: Multiplication and Division by 6 and 7

Build fluency with multiplication and division facts using units of 6.

3.OA.A.4 3.OA.C.7

Build fluency with multiplication and division facts using units of 7.

3.OA.A.4 3.OA.C.7

Use the associative property as a strategy to multiply by units of 6.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 6.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 7.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Solve one- and two-step word problems involving units up to 7.

3.OA.A.3 3.OA.D.8

Topic C: Multiplication and Division by 8 and 9

Build fluency with multiplication and division facts using units of 8 and 9.

3.OA.A.4 3.OA.C.7

Use the associative property as a strategy to multiply by units of 8 and 9.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 8 and 9.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 8 and 9, including the subtractive use of the distributive property.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Solve one- and two-step word problems involving units up to 9.

3.OA.A.3 3.OA.D.8

Topic D: Multiplication and Division by Values Greater than 10

Multiply one-digit whole numbers by multiples of 10.

3.NBT.A.3 3.OA.A.4 3.OA.B.5

Multiply one-digit whole numbers by two-digit whole numbers using the associative and distributive properties.

3.NBT.A.3 3.OA.A.4 3.OA.B.5

Topic E: Two-Step Word Problems and Patterns in Arithmetic

Solve two-step word problems involving all four operations.

3.OA.D.8

Solve two-step word problems involving all four operations, including multiplying one-digit whole numbers by multiples of 10.

3.NBT.A.3 3.OA.D.8

Identify patterns in single or multiple rows/columns of the multiplication table.

3.OA.C.7 3.OA.D.9

Identify other patterns in the multiplication table.

3.OA.D.9

Identify arithmetic patterns and explain them using properties of operations.

3.OA.D.9

Multiplication and Division, Part 2

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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